COVAR in WPS Spreadsheet: Population Covariance of Paired Data
Calculate population covariance from paired integer observations, understand the divisor and units, and distinguish covariance from correlation.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
COVAR measures the average product of two variables’ deviations from their respective means. Positive covariance indicates that above-average values tend to occur together in the supplied pairs; negative covariance indicates opposing deviations. Its magnitude depends on the measurement scales.
The WPS lesson uses the population divisor n, not the sample divisor n − 1. It explicitly describes integer inputs, so the examples here retain fully numeric integer pairs. They do not establish behavior for fractional observations or mixed text and numeric ranges.
Syntax and paired layout
=COVAR(array1, array2)
Each argument supplies one variable’s observations. Keep corresponding observations on the same row and both ranges the same size. Do not sort one column independently: that changes the pairings and therefore the result.
Enter this original dataset:
| Row | A: x | B: y |
|---|---|---|
| 2 | 1 | 2 |
| 3 | 2 | 4 |
| 4 | 3 | 6 |
- Enter
=COVAR(A2:A4,B2:B4)in D2. - The independent expected result is 4/3, approximately 1.33333333333333.
- Label it covariance in x-units × y-units. It is not a percentage or a standardized correlation coefficient.
The independent calculation uses x mean 2 and y mean 4. The products of centered deviations are 2, 0 and 2. Their sum is 4; dividing by three pairs gives 4/3. Dividing by two would instead compute a different sample statistic.
Original controls
Each row below is a separate replacement dataset for A2:A4 and B2:B4, using the same formula.
| x values | y values | Expected covariance |
|---|---|---|
| 1, 2, 3 | 2, 4, 6 | 4/3 |
| 1, 2, 3 | 6, 4, 2 | −4/3 |
| 1, 2, 3 | 4, 4, 4 | 0 |
| −1, 0, 1 | 1, 0, 1 | 0 |
| 11, 12, 13 | 102, 104, 106 | 4/3 |
| 1, 2, 3 | 4, 8, 12 | 8/3 |
The fourth row is particularly useful: y is x squared, yet covariance is zero. Zero covariance does not establish independence or absence of a nonlinear relationship.
Practical scaling and interpretation
Adding a constant to either series does not change its centered deviations. This explains why the fifth dataset has the same covariance as the first. Multiplying y by two doubles covariance, as shown in the last dataset. Changing units can therefore change the numerical result without changing the underlying relationship.
For standardized comparison, CORREL answers a different question. For a fitted line’s constant term, see INTERCEPT. Neither covariance nor correlation alone proves causality.
Documentation checks and troubleshooting
The official walkthrough uses x = 2, 4, 6, 8, 10 and y = 1, 3, 5, 7, 9, displaying 8. Independent centered products sum to 40 and divide by five to give 8, corroborating the population formula shown in the lesson.
The lesson documents #N/A for unequal numbers of data points and #DIV/0! for an empty array. It says text, logical values and empty cells are ignored, while zero is included. Those statements do not establish how arbitrary differently placed nonnumeric entries are paired. Clean both columns together and use aligned numeric observations rather than relying on unverified mixed-value alignment. A constant variable gives zero covariance for the complete numeric examples here; that is different from correlation’s zero-standard-deviation problem.
Availability and evidence scope
The official WPS lesson is dated 2019-06-14. The lesson explicitly applies to WPS Office for Windows Personal. A numeric build is not specified. The lesson date is a documented-by date, not a first-release date. First introduction, last functioning version and retirement or deprecation history remain unestablished. No cross-platform parity is inferred.
The complete lesson and its formula images or walkthrough were inspected on October 18, 2026. Original examples in this guide were independently calculated from the documented model; they were not executed in WPS or another spreadsheet engine. Historical vendor demonstrations are identified separately. Numeric approximations below are independent expectations, not promises about WPS display precision.